Background

This document has nls (non-linear least squares) regression fits to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass vs. stand age relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.

We considered the following Michaelis-Menten functional form \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left( \frac{A \cdot STDAGE_{t2}}{k+STDAGE_{t2}}\right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(STDAGE_{t2}\) is the stand age at the second of two FIA plot tree censuses, and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(\tau\): biomass productivity trend, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.

Data have increasing variance in \(B\) with increasing \(STDAGE_{t2}\), thus, weighted-nls is the best approach. We explored a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}^2\) in equal-sample sized stand age bins (n=20 where possible, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.

Model selection is used to determine the best fitting models, which is implemented in three parts. The first part selects the best model form using \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest).

model 1: simple model \(B = (1 + (yr-1990)* \tau/100) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

model 2: alpha model \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

Then, model selection part two takes the best fitting model from part 1 and and adds the \(p\) and \(s\) parameters (individually then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.

sub-model a: p form \(pA + \left( \frac {(1-p) * A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

sub-model b: s form \(\left( \frac {A \cdot STDAGE_{t2}^s} {k^s+STDAGE_{t2}^s} \right)\)

sub-model c: p and s together \(pA + \left( \frac {(1-p) *A \cdot STDAGE_{t2}^s} {k^s + STDAGE_{t1}^s} \right)\)

Lastly, model selection part 3, fits three similar models to model selection part one, but uses the Log-Normal functional form. The Log-Normal equation fits more of “hump-shaped” curve which allows for a decrease in biomass at old stand ages. Two Log-normal models are fitted: 1) the simple model, and 2) the \(\alpha\) model: account for growth compensation due to plot biomass loss.

model 4: simple model \(B = (1 + (yr-1990)* \tau/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)

model 5: alpha model \(B = (1 + (yr-1990)* \tau/100) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)

Note:

This analysis only uses plot biomass data from the same plot locations and measurement intervals for which we also have data on biomass growth (which is used in the growth vs. biomass analysis ). We use the second of the two plot measurements comprising a \(G\) interval

This includes the following plot-based filtering criteria (which were used for the growth vs. biomass analysis):

exclude FIA plots in plantation forests
exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6880     1758.3                                
## 2   6879     1588.0  1 170.38  738.11 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 74579.98
## 2     2 73880.45

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.69176    0.17752   3.897 9.84e-05 ***
## alpha   0.83853    0.02819  29.742  < 2e-16 ***
## A     416.54207   27.03681  15.406  < 2e-16 ***
## k     188.16891   13.29611  14.152  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4805 on 6879 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 9.098e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   6879     1588.0                          
## 2   6878     1587.8  1 0.10967   0.475 0.4907
##   model      AIC
## 1     2 73880.45
## 2    2a 73881.97
## 3    2b 73864.22
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.64525    0.17419   3.704 0.000214 ***
## alpha   0.84366    0.02836  29.752  < 2e-16 ***
## A     267.35244   24.48232  10.920  < 2e-16 ***
## k      87.16041   11.89186   7.329 2.58e-13 ***
## s       1.22609    0.05764  21.273  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4799 on 6878 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.167e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6878     1726.3                                
## 2   6877     1557.0  1 169.29  747.71 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 73864.22
## 2     3 74457.48
## 3     4 73749.07

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.81288    0.18481   4.398 1.11e-05 ***
## alpha   0.83154    0.02775  29.971  < 2e-16 ***
## a      31.22968    1.70998  18.263  < 2e-16 ***
## b     112.93234    5.39611  20.928  < 2e-16 ***
## c     123.66007    5.88096  21.027  < 2e-16 ***
## d       1.06739    0.04852  21.999  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4758 on 6877 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  21456     6780.2                                
## 2  21455     6542.2  1 237.98  780.44 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 223452.5
## 2     2 222687.8

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.95393    0.10285   9.275   <2e-16 ***
## alpha   0.76407    0.02559  29.853   <2e-16 ***
## A     167.63507    4.38459  38.233   <2e-16 ***
## k      78.56108    2.47525  31.739   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5522 on 21455 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.327e-06
##   (1226 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  21455     6542.2                                
## 2  21454     6515.0  1 27.151  89.409 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 222687.8
## 2    2a 222600.5
## 3    2b 222539.7
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.06559    0.10698   9.961   <2e-16 ***
## alpha   0.76996    0.02564  30.034   <2e-16 ***
## A     115.78050    3.70206  31.275   <2e-16 ***
## k      40.57330    1.64862  24.610   <2e-16 ***
## s       1.41290    0.04066  34.748   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5503 on 21454 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 4.417e-06
##   (1226 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  21454     6676.2                                
## 2  21453     6430.8  1 245.39  818.61 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 222539.7
## 2     3 223124.9
## 3     4 222323.3

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.07103    0.10677   10.03   <2e-16 ***
## alpha   0.77321    0.02528   30.59   <2e-16 ***
## a      22.95843    0.83356   27.54   <2e-16 ***
## b      67.52314    1.55360   43.46   <2e-16 ***
## c     103.10031    2.16612   47.60   <2e-16 ***
## d       1.08732    0.02951   36.85   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5475 on 21453 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1226 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6934    1078.14                                
## 2   6933     950.93  1 127.21  927.46 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 75745.30
## 2     2 74876.34

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.16754    0.11201   1.496    0.135    
## alpha   0.88651    0.02699  32.844   <2e-16 ***
## A     438.44852   23.33717  18.788   <2e-16 ***
## k     125.86939    8.34455  15.084   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3704 on 6933 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.061e-06
##   (370 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6933     950.93                                
## 2   6932     944.77  1 6.1579  45.182 1.938e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 74876.34
## 2    2a 74833.27
## 3    2b       NA
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.19985    0.11340   1.762  0.07805 .  
## alpha   0.88716    0.02706  32.787  < 2e-16 ***
## A     297.82149   16.82169  17.705  < 2e-16 ***
## k      36.53118    7.80982   4.678 2.96e-06 ***
## p      -0.36908    0.11916  -3.097  0.00196 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3692 on 6932 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 4.535e-06
##   (370 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6932    1067.83                                
## 2   6931     941.94  1 125.89  926.36 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 74833.27
## 2     3 75682.64
## 3     4 74814.41

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.19868    0.11312   1.756   0.0791 .  
## alpha   0.88629    0.02701  32.817  < 2e-16 ***
## a      46.50096   10.46650   4.443 9.02e-06 ***
## b     143.42164   12.84562  11.165  < 2e-16 ***
## c     119.23589    8.07145  14.773  < 2e-16 ***
## d       1.10698    0.12085   9.160  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3686 on 6931 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (370 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5547     1704.0                                
## 2   5546     1616.1  1 87.972   301.9 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 59908.34
## 2     2 59616.16

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.97722    0.20650   4.732 2.28e-06 ***
## alpha   0.83417    0.04432  18.822  < 2e-16 ***
## A     365.92255   32.26558  11.341  < 2e-16 ***
## k     190.74942   19.15547   9.958  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5398 on 5546 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 4.557e-06
##   (296 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5546     1616.1                                
## 2   5545     1585.5  1 30.557  106.87 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 59616.16
## 2    2a 59512.21
## 3    2b       NA
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.06896    0.21114   5.063 4.26e-07 ***
## alpha   0.86162    0.04368  19.726  < 2e-16 ***
## A     194.67994   12.87743  15.118  < 2e-16 ***
## k      40.40127    6.99591   5.775 8.11e-09 ***
## p      -0.33156    0.07736  -4.286 1.85e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5347 on 5545 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 4.118e-06
##   (296 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5545     1667.1                                
## 2   5544     1570.6  1 96.455  340.47 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 59512.21
## 2     3 59790.56
## 3     4 59461.77

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.06254    0.20963   5.069 4.14e-07 ***
## alpha   0.87213    0.04334  20.125  < 2e-16 ***
## a      19.41594    3.70394   5.242 1.65e-07 ***
## b      96.66094    5.38215  17.960  < 2e-16 ***
## c     101.25661    4.50967  22.453  < 2e-16 ***
## d       1.02471    0.07125  14.382  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5323 on 5544 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (296 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9432     1587.5                                
## 2   9431     1471.4  1 116.06  743.86 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 98445.42
## 2     2 97731.13

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.9572     0.1106   8.651   <2e-16 ***
## alpha   0.7909     0.0270  29.288   <2e-16 ***
## A     179.3531     5.9484  30.152   <2e-16 ***
## k      52.8587     2.8565  18.505   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.395 on 9431 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.096e-07
##   (571 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9431     1471.4                                
## 2   9430     1465.8  1 5.5843  35.925 2.126e-09 ***
## 3   9430     1465.3  0 0.0000                      
## 4   9429     1465.2  1 0.0872   0.561    0.4539    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 97731.13
## 2    2a 97697.26
## 3    2b 97693.91
## 4    2c 97695.35

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.96491    0.11082   8.707   <2e-16 ***
## alpha   0.79208    0.02697  29.372   <2e-16 ***
## A     128.12523    4.67964  27.379   <2e-16 ***
## k      32.43433    0.96401  33.645   <2e-16 ***
## s       1.85487    0.14913  12.438   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3942 on 9430 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.503e-06
##   (571 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9430     1580.5                                
## 2   9429     1464.6  1 115.85  745.85 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 97693.91
## 2     3 98407.53
## 3     4 97691.25

## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "223", :
## provided 32 variables to replace 31 variables

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.95467    0.11054   8.637  < 2e-16 ***
## alpha   0.79131    0.02698  29.328  < 2e-16 ***
## a      14.36005   24.74403   0.580    0.562    
## b     100.63809   25.72856   3.912 9.24e-05 ***
## c     118.73960   12.04638   9.857  < 2e-16 ***
## d       1.55264    0.35970   4.316 1.60e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3941 on 9429 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (571 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12112     2738.8                                
## 2  12111     2512.1  1 226.69  1092.9 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 130399.6
## 2     2 129354.9

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.31050    0.12159   10.78   <2e-16 ***
## alpha   0.71119    0.01999   35.59   <2e-16 ***
## A     278.85285    8.36741   33.33   <2e-16 ***
## k      76.76299    2.35893   32.54   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4554 on 12111 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.78e-06
##   (729 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1  12111     2512.1                               
## 2  12110     2485.7  1 26.3813 128.5253 <2e-16 ***
## 3  12109     2485.6  1  0.0694   0.3383 0.5608    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 129354.9
## 2    2a 129229.0
## 3    2b       NA
## 4    2c 129230.7

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau     1.296348   0.120428  10.765   <2e-16 ***
## alpha   0.718309   0.020363  35.275   <2e-16 ***
## A     220.176569   6.649464  33.112   <2e-16 ***
## k      42.722737   2.304084  18.542   <2e-16 ***
## p      -0.062849   0.007588  -8.283   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4531 on 12110 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.038e-06
##   (729 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12110     2709.7                                
## 2  12109     2486.7  1 223.02    1086 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 129229.0
## 2     3 130274.4
## 3     4 129235.9

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau     1.296348   0.120428  10.765   <2e-16 ***
## alpha   0.718309   0.020363  35.275   <2e-16 ***
## A     220.176569   6.649464  33.112   <2e-16 ***
## k      42.722737   2.304084  18.542   <2e-16 ***
## p      -0.062849   0.007588  -8.283   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4531 on 12110 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.038e-06
##   (729 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12427     4751.2                                
## 2  12426     4496.0  1 255.23  705.42 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 137630.1
## 2     2 136945.7

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.79958    0.13463   5.939 2.94e-09 ***
## alpha   0.66173    0.02305  28.704  < 2e-16 ***
## A     296.34997   11.52223  25.720  < 2e-16 ***
## k      81.84131    3.24704  25.205  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6015 on 12426 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.623e-06
##   (737 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  12426     4496.0                                 
## 2  12425     4481.7  1 14.2985 39.6414 3.154e-10 ***
## 3  12425     4479.1  0  0.0000                      
## 4  12424     4479.0  1  0.1142  0.3168    0.5735    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 136945.7
## 2    2a 136908.1
## 3    2b 136901.1
## 4    2c 136902.8

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.79154    0.13392   5.911  3.5e-09 ***
## alpha   0.67002    0.02357  28.426  < 2e-16 ***
## A     206.16286    9.61009  21.453  < 2e-16 ***
## k      41.26733    2.85865  14.436  < 2e-16 ***
## s       1.22628    0.03283  37.347  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6004 on 12425 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.442e-06
##   (737 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12425     4726.6                                
## 2  12424     4479.2  1 247.46  686.39 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 136901.1
## 2     3 137569.6
## 3     4 136903.2

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.79154    0.13392   5.911  3.5e-09 ***
## alpha   0.67002    0.02357  28.426  < 2e-16 ***
## A     206.16286    9.61009  21.453  < 2e-16 ***
## k      41.26733    2.85865  14.436  < 2e-16 ***
## s       1.22628    0.03283  37.347  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6004 on 12425 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.442e-06
##   (737 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

234 - lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1273     342.72                                
## 2   1272     305.18  1 37.541  156.47 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14240.14
## 2     2 14094.10

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.52561    0.40921   1.284    0.199    
## alpha   0.79999    0.05788  13.821  < 2e-16 ***
## A     478.26877   81.98228   5.834 6.86e-09 ***
## k     153.20836   30.69689   4.991 6.84e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4898 on 1272 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.326e-06
##   (68 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_234,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_234,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   1272     305.18                          
## 2   1271     304.82  1 0.35578  1.4835 0.2235
##   model      AIC
## 1     2 14094.10
## 2    2a 14094.62
## 3    2b       NA
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.52561    0.40921   1.284    0.199    
## alpha   0.79999    0.05788  13.821  < 2e-16 ***
## A     478.26877   81.98228   5.834 6.86e-09 ***
## k     153.20836   30.69689   4.991 6.84e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4898 on 1272 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.326e-06
##   (68 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

model selection 3

## Error in nls(f_3, data = G_234, start = c(tau = tau.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model      AIC
## 1     2 14094.10
## 2     3       NA
## 3     4 14096.77

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.52561    0.40921   1.284    0.199    
## alpha   0.79999    0.05788  13.821  < 2e-16 ***
## A     478.26877   81.98228   5.834 6.86e-09 ***
## k     153.20836   30.69689   4.991 6.84e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4898 on 1272 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.326e-06
##   (68 observations deleted due to missingness)

summary

simple log-normal model: does not fit
log-normal alpha model: fits

predict and plot

`## plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

simple model: does not fit
alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

model selection 3

summary

simple log-normal model: does not fit
log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2165     468.74                                
## 2   2164     449.79  1 18.948   91.16 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 22573.55
## 2     2 22486.10

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.30617    0.21270   1.439     0.15    
## alpha   0.70921    0.06963  10.186   <2e-16 ***
## A     234.25380   19.13609  12.241   <2e-16 ***
## k      86.34944    9.58196   9.012   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4559 on 2164 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.498e-06
##   (122 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2164     449.79                                
## 2   2163     442.07  1 7.7182  37.764 9.477e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 22486.10
## 2    2a 22450.57
## 3    2b 22453.39
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.40256    0.21862   1.841   0.0657 .  
## alpha   0.71553    0.06967  10.270   <2e-16 ***
## A     148.57344   10.23035  14.523   <2e-16 ***
## k       5.24468    5.41531   0.968   0.3329    
## p      -3.23715    3.60610  -0.898   0.3695    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4521 on 2163 degrees of freedom
## 
## Number of iterations to convergence: 18 
## Achieved convergence tolerance: 8.969e-06
##   (122 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2163     462.14                                
## 2   2162     443.26  1 18.877  92.069 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 22450.57
## 2     3 22546.83
## 3     4 22458.41

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.40256    0.21862   1.841   0.0657 .  
## alpha   0.71553    0.06967  10.270   <2e-16 ***
## A     148.57344   10.23035  14.523   <2e-16 ***
## k       5.24468    5.41531   0.968   0.3329    
## p      -3.23715    3.60610  -0.898   0.3695    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4521 on 2163 degrees of freedom
## 
## Number of iterations to convergence: 18 
## Achieved convergence tolerance: 8.969e-06
##   (122 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    708     336.70                                
## 2    707     329.96  1 6.7436  14.449 0.0001564 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7311.058
## 2     2 7298.673

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.2620     0.4735  -0.553  0.58018    
## alpha   0.4666     0.1144   4.077 5.07e-05 ***
## A     317.9208    75.0171   4.238 2.55e-05 ***
## k     133.3036    34.6376   3.849  0.00013 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6832 on 707 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 4.037e-06
##   (3 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    707     329.96                          
## 2    706     329.85  1 0.10851  0.2322   0.63
##   model      AIC
## 1     2 7298.673
## 2    2a 7300.439
## 3    2b       NA
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.2620     0.4735  -0.553  0.58018    
## alpha   0.4666     0.1144   4.077 5.07e-05 ***
## A     317.9208    75.0171   4.238 2.55e-05 ***
## k     133.3036    34.6376   3.849  0.00013 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6832 on 707 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 4.037e-06
##   (3 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    706     321.06                                
## 2    705     310.62  1 10.448  23.714 1.381e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 7298.673
## 2     3 7281.242
## 3     4 7259.720

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -0.3313     0.4397  -0.754    0.451    
## alpha   0.5608     0.1051   5.333 1.30e-07 ***
## a      11.8038     1.9008   6.210 9.06e-10 ***
## b      88.9590    10.2328   8.693  < 2e-16 ***
## c      58.2985     5.0380  11.572  < 2e-16 ***
## d       1.0553     0.0947  11.143  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6638 on 705 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

simple model: does not fit
alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (only 64 observations)

model selection 3

summary

simple log-normal model: does not fit
log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

262 - California Dry Steppe

model selection 1

summary

simple model: does not fit
alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (0 observations)

model selection 3

summary

simple log-normal model: does not fit
log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    155     28.883                              
## 2    154     27.554  1 1.3296  7.4314 0.007153 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1995.769
## 2     2 1990.323

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)   
## tau      1.2518     2.1470   0.583  0.56070   
## alpha    0.7269     0.2520   2.885  0.00448 **
## A     5419.6547  2776.6065   1.952  0.05276 . 
## k     1453.0069   510.1242   2.848  0.00500 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.423 on 154 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 4.387e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_263,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_263,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1    154     27.554                             
## 2    153     26.681  1 0.87281  5.0051 0.02672 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 1990.323
## 2    2a 1987.237
## 3    2b       NA
## 4    2c       NA

## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "263", :
## provided 32 variables to replace 31 variables

## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "263", :
## provided 32 variables to replace 31 variables

## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "263", :
## provided 32 variables to replace 31 variables

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   1.752e+00  2.562e+00   0.684 0.495280    
## alpha 8.326e-01  2.442e-01   3.410 0.000831 ***
## A     1.590e+04  2.006e+04   0.793 0.429275    
## k     5.997e+03  7.916e+03   0.758 0.449878    
## p     2.363e-03  2.414e-03   0.979 0.329190    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4176 on 153 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.066e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)   
## 1    153     30.979                             
## 2    152     29.287  1 1.6923  8.7832 0.00353 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 1987.237
## 2     3 2010.835
## 3     4 2003.960

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   1.752e+00  2.562e+00   0.684 0.495280    
## alpha 8.326e-01  2.442e-01   3.410 0.000831 ***
## A     1.590e+04  2.006e+04   0.793 0.429275    
## k     5.997e+03  7.916e+03   0.758 0.449878    
## p     2.363e-03  2.414e-03   0.979 0.329190    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4176 on 153 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.066e-06
##   (1 observation deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    214     67.657                           
## 2    213     67.621  1 0.036228  0.1141 0.7358
##   model      AIC
## 1     1 2322.942
## 2     2 2324.826

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)  
## tau  -0.8160     0.9509  -0.858   0.3918  
## A   277.8964   110.6751   2.511   0.0128 *
## k   159.0901    64.0178   2.485   0.0137 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5623 on 214 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.666e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    214     67.657                          
## 2    213     67.505  1 0.15278  0.4821 0.4882
##   model      AIC
## 1     1 2322.942
## 2    1a 2324.452
## 3    1b       NA
## 4    1c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)  
## tau  -0.8160     0.9509  -0.858   0.3918  
## A   277.8964   110.6751   2.511   0.0128 *
## k   159.0901    64.0178   2.485   0.0137 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5623 on 214 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.666e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    212     62.692                          
## 2    211     62.465  1 0.22643  0.7649 0.3828
##   model      AIC
## 1     1 2322.942
## 2     3 2310.402
## 3     4 2311.616

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * 
##     exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## tau  -1.45035    0.59364  -2.443 0.015377 *  
## a    40.15842   12.25407   3.277 0.001225 ** 
## b   148.91132   39.27593   3.791 0.000195 ***
## c   142.76710    8.69554  16.418  < 2e-16 ***
## d     0.64093    0.09421   6.803 1.03e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5438 on 212 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

simple model: does not fit
alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

model selection 3

summary

simple log-normal model: does not fit
log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

summary

simple model: does not fit
alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

model selection 3

summary

simple log-normal model: does not fit
log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

322 - American Semidesert and Desert

model selection 1

## Error in nls(f_1, data = G_322, start = c(tau = tau.start, A = A.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

##   model AIC
## 1     1  NA
## 2     2  NA

## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in get(paste("nls_322.", Mod.Sel1, sep = "")) : 
##   object 'nls_322.' not found

summary

simple model: does not fit
alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

model selection 3

summary

simple log-normal model: does not fit
log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

Cannot fit model
not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

simple model: does not fit
alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

model selection 3

summary

simple log-normal model: does not fit
log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

332 - Great Plains Steppe

Cannot fit model

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    205     109.38                            
## 2    204     107.28  1 2.0903  3.9748 0.04752 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2230.704
## 2     2 2228.690

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau     0.4762     1.5880   0.300    0.765  
## alpha   0.6443     0.2929   2.200    0.029 *
## A     502.5964   606.4813   0.829    0.408  
## k     360.7593   468.4009   0.770    0.442  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7252 on 204 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.93e-06
##   (24 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_332,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model     AIC
## 1     2 2228.69
## 2    2a      NA
## 3    2b      NA
## 4    2c      NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau     0.4762     1.5880   0.300    0.765  
## alpha   0.6443     0.2929   2.200    0.029 *
## A     502.5964   606.4813   0.829    0.408  
## k     360.7593   468.4009   0.770    0.442  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7252 on 204 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.93e-06
##   (24 observations deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

model selection 3

## Error in nls(f_3, data = G_332, start = c(tau = tau.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_4, data = G_332, start = c(tau = tau.start, alpha = alpha.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model     AIC
## 1     2 2228.69
## 2     3      NA
## 3     4      NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## tau     0.4762     1.5880   0.300    0.765  
## alpha   0.6443     0.2929   2.200    0.029 *
## A     502.5964   606.4813   0.829    0.408  
## k     360.7593   468.4009   0.770    0.442  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7252 on 204 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.93e-06
##   (24 observations deleted due to missingness)

summary

simple log-normal model: does not fit
log-normal alpha model: does not fit

predict and plot

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

simple model: does not fit
alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

model selection 3

summary

simple log-normal model: does not fit
log-normal alpha model: does not fit
model not fitted because only 62 observations

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

342 - Intermountain Semi-Desert

model selection 1

summary

simple model: does not fit
alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

model selection 3

summary

simple log-normal model: does not fit
log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

411 - Everglades

model selection 1

summary

simple model: does not fit
alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

model selection 3

summary

simple log-normal model: does not fit
log-normal alpha model: does not fit

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6772     1333.1                                
## 2   6771     1152.4  1 180.72  1061.8 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 71776.53
## 2     2 70791.58

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.83471    0.16884   4.944 7.84e-07 ***
## alpha   0.80612    0.02248  35.855  < 2e-16 ***
## A     416.13390   24.57826  16.931  < 2e-16 ***
## k     192.41525   11.49858  16.734  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4125 on 6771 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.492e-06
##   (3 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6771     1152.4                                
## 2   6770     1144.3  1 8.0931  47.881 4.944e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 70791.58
## 2    2a 70745.83
## 3    2b       NA
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau     0.720852   0.161462   4.465 8.15e-06 ***
## alpha   0.814665   0.022641  35.982  < 2e-16 ***
## A     311.623953  18.279896  17.047  < 2e-16 ***
## k     106.277700  10.003747  10.624  < 2e-16 ***
## p      -0.044463   0.009478  -4.691 2.77e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4111 on 6770 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.248e-06
##   (3 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6770     1322.9                                
## 2   6769     1140.1  1 182.86  1085.7 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 70745.83
## 2     3 71728.53
## 3     4 70722.69

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.72103    0.16125   4.471 7.90e-06 ***
## alpha   0.81660    0.02244  36.392  < 2e-16 ***
## a      11.86910    2.87240   4.132 3.64e-05 ***
## b     156.98730   10.86890  14.444  < 2e-16 ***
## c     207.69052   26.59499   7.809 6.62e-15 ***
## d       1.72266    0.11349  15.179  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4104 on 6769 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7751     1167.8                                
## 2   7750     1080.3  1 87.472  627.52 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 85843.11
## 2     2 85241.40

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.91183    0.12119   7.524 5.91e-14 ***
## alpha   0.90018    0.03388  26.571  < 2e-16 ***
## A     223.88494    7.41504  30.193  < 2e-16 ***
## k      43.44403    2.42381  17.924  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3734 on 7750 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.246e-06
##   (432 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_M221,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7750     1080.3                                
## 2   7748     1066.6  2 13.731  49.874 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 85241.40
## 2    2a       NA
## 3    2b 85154.38
## 4    2c 85146.21

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.99857    0.12481   8.001 1.41e-15 ***
## alpha   0.89771    0.03372  26.622  < 2e-16 ***
## A     154.79938    4.49176  34.463  < 2e-16 ***
## k      44.43699    2.39761  18.534  < 2e-16 ***
## p       0.40664    0.05999   6.779 1.30e-11 ***
## s       3.75774    0.53787   6.986 3.06e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.371 on 7748 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 9.783e-06
##   (432 observations deleted due to missingness)

summary

add p model: does not fit
add s model: fits
add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7749     1151.2                                
## 2   7748     1064.1  1 87.036  633.71 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 85146.21
## 2     3 85736.15
## 3     4 85128.55

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.99348    0.12427   7.994 1.49e-15 ***
## alpha   0.89846    0.03365  26.700  < 2e-16 ***
## a      49.42999   12.68864   3.896 9.88e-05 ***
## b     102.10729   12.62474   8.088 6.99e-16 ***
## c     100.61164    3.18931  31.547  < 2e-16 ***
## d       1.10537    0.12889   8.576  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3706 on 7748 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (432 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    887     122.26                                
## 2    886     106.68  1 15.583  129.42 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9055.244
## 2     2 8935.898

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.01094    0.25540  -0.043    0.966    
## alpha   0.89519    0.07261  12.329  < 2e-16 ***
## A     292.54555   34.23433   8.545  < 2e-16 ***
## k      95.82504   15.20296   6.303  4.6e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.347 on 886 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.455e-06
##   (3 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1    886     106.68                             
## 2    885     106.00  1 0.67604  5.6442 0.01773 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 8935.898
## 2    2a 8932.240
## 3    2b       NA
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.04774    0.26180   0.182   0.8553    
## alpha   0.90336    0.07277  12.413  < 2e-16 ***
## A     225.89814   25.25934   8.943  < 2e-16 ***
## k      51.43265   12.26266   4.194 3.01e-05 ***
## p      -0.08665    0.04437  -1.953   0.0512 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3461 on 885 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.431e-06
##   (3 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    885     121.92                                
## 2    884     106.29  1 15.629  129.98 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 8932.240
## 2     3 9056.791
## 3     4 8936.700

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.04774    0.26180   0.182   0.8553    
## alpha   0.90336    0.07277  12.413  < 2e-16 ***
## A     225.89814   25.25934   8.943  < 2e-16 ***
## k      51.43265   12.26266   4.194 3.01e-05 ***
## p      -0.08665    0.04437  -1.953   0.0512 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3461 on 885 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.431e-06
##   (3 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    955     204.76                                
## 2    954     190.05  1 14.711  73.843 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9951.187
## 2     2 9881.765

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.46206    0.43464   1.063    0.288    
## alpha   0.77623    0.08421   9.218  < 2e-16 ***
## A     306.46634   52.06959   5.886 5.48e-09 ***
## k     133.47106   25.97517   5.138 3.36e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4463 on 954 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.065e-06
##   (51 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M231,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    954     190.05                          
## 2    953     189.87  1 0.18837  0.9455 0.3311
##   model      AIC
## 1     2 9881.765
## 2    2a 9882.815
## 3    2b 9883.524
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.46206    0.43464   1.063    0.288    
## alpha   0.77623    0.08421   9.218  < 2e-16 ***
## A     306.46634   52.06959   5.886 5.48e-09 ***
## k     133.47106   25.97517   5.138 3.36e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4463 on 954 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.065e-06
##   (51 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

model selection 3

## Error in nls(f_4, data = G_M231, start = c(tau = tau.start, alpha = alpha.start,  : 
##   Convergence failure: singular convergence (7)
##   model      AIC
## 1     2 9881.765
## 2     3 9954.667
## 3     4       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.46206    0.43464   1.063    0.288    
## alpha   0.77623    0.08421   9.218  < 2e-16 ***
## A     306.46634   52.06959   5.886 5.48e-09 ***
## k     133.47106   25.97517   5.138 3.36e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4463 on 954 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.065e-06
##   (51 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: does not fit

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3298     2133.7                                
## 2   3297     2025.3  1 108.38  176.43 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 43707.67
## 2     2 43537.59

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau   5.191e-01  6.682e-01   0.777    0.437    
## alpha 1.013e+00  6.953e-02  14.570  < 2e-16 ***
## A     1.011e+03  1.753e+02   5.765 8.94e-09 ***
## k     3.764e+02  3.589e+01  10.485  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7838 on 3297 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.623e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3297     2025.3                                
## 2   3296     1977.6  1 47.753  79.588 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 43537.59
## 2    2a 43460.83
## 3    2b 43454.65
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.53718    0.65998   0.814    0.416    
## alpha   1.07143    0.06934  15.451  < 2e-16 ***
## A     536.31143   86.55496   6.196  6.5e-10 ***
## k     119.02407   10.27404  11.585  < 2e-16 ***
## s       1.45921    0.05940  24.566  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7739 on 3296 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 1.462e-06
##   (2 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3296     2088.0                                
## 2   3295     1970.6  1  117.4   196.3 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2b 43454.65
## 2     3 43640.14
## 3     4 43451.11

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.5901     0.6749   0.874    0.382    
## alpha   1.0753     0.0695  15.472  < 2e-16 ***
## a       0.0000     5.4149   0.000    1.000    
## b     467.6358    77.2386   6.054 1.57e-09 ***
## c     581.4147   102.1728   5.691 1.38e-08 ***
## d       2.0957     0.1343  15.603  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7733 on 3295 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1983     1184.8                                
## 2   1982     1168.9  1 15.894   26.95 2.302e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24895.19
## 2     2 24870.37

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     7.8534     4.3636   1.800  0.07205 .  
## alpha   0.6133     0.1100   5.576 2.80e-08 ***
## A     145.3203    54.2373   2.679  0.00744 ** 
## k     128.1086    16.9324   7.566 5.86e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.768 on 1982 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.423e-06
##   (7 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   1982     1168.9                            
## 2   1981     1166.8  1 2.1673  3.6797 0.05522 .
## 3   1981     1168.2  0 0.0000                  
## 4   1980     1166.2  1 2.0169  3.4243 0.06439 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 24870.37
## 2    2a 24868.68
## 3    2b 24871.21
## 4    2c 24869.78

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     7.87846    4.37803   1.800  0.07208 .  
## alpha   0.62355    0.11083   5.626 2.10e-08 ***
## A     130.60786   48.82237   2.675  0.00753 ** 
## k      90.96584   18.25938   4.982 6.84e-07 ***
## p      -0.06446    0.03772  -1.709  0.08758 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7674 on 1981 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.152e-06
##   (7 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1   1981     1182.3                               
## 2   1980     1166.2  1 16.138    27.4 1.83e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 24868.68
## 2     3 24894.97
## 3     4 24869.67

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     7.87846    4.37803   1.800  0.07208 .  
## alpha   0.62355    0.11083   5.626 2.10e-08 ***
## A     130.60786   48.82237   2.675  0.00753 ** 
## k      90.96584   18.25938   4.982 6.84e-07 ***
## p      -0.06446    0.03772  -1.709  0.08758 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7674 on 1981 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.152e-06
##   (7 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

Model selection 1

summary

simple model: does not fit
alpha model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

model selection 3

summary

simple log-normal model: does not fit
log-normal alpha model: does not fit
model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    363     122.71                                
## 2    362     118.32  1 4.3863  13.419 0.0002862 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3833.912
## 2     2 3822.590

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.9293     0.3039  -6.349 6.49e-10 ***
## alpha   0.5582     0.1420   3.930 0.000102 ***
## A     574.0776   210.6322   2.725 0.006732 ** 
## k     232.2820   111.8287   2.077 0.038495 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5717 on 362 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.569e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_M313,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)  
## 1    362     118.32                           
## 2    361     116.79  1 1.5355  4.7465   0.03 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 3822.590
## 2    2a 3819.809
## 3    2b       NA
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau     -1.94798    0.29564  -6.589 1.57e-10 ***
## alpha    0.59640    0.13334   4.473 1.04e-05 ***
## A     1027.37948  910.11547   1.129    0.260    
## k      568.28926  621.17133   0.915    0.361    
## p        0.02248    0.01655   1.358    0.175    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5688 on 361 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.979e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    361     120.72                                
## 2    360     115.26  1 5.4536  17.034 4.567e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 3819.809
## 2     3 3831.912
## 3     4 3816.992

## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "M313", :
## provided 32 variables to replace 31 variables

## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "M313", :
## provided 32 variables to replace 31 variables

## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Ecoprovince == "M313", :
## provided 32 variables to replace 31 variables

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.8271     0.3338  -5.473 8.29e-08 ***
## alpha   0.6108     0.1286   4.749 2.96e-06 ***
## a      42.6892    11.0490   3.864 0.000132 ***
## b     180.7375    41.0611   4.402 1.42e-05 ***
## c     177.7659    40.8862   4.348 1.79e-05 ***
## d       0.9807     0.2073   4.730 3.23e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5658 on 360 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1736     651.22                                
## 2   1735     600.64  1 50.579   146.1 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18138.23
## 2     2 17999.63

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.85360    0.35023  -2.437   0.0149 *  
## alpha   0.59310    0.04314  13.747  < 2e-16 ***
## A     274.07835   36.52316   7.504 9.82e-14 ***
## k     131.06768   13.53831   9.681  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5884 on 1735 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.714e-06
##   (18 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Warning in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M331, : No starting values specified for some parameters.
## Initializing 'tau', 'p', 'A', 's', 'k' to '1.'.
## Consider specifying 'start' or using a selfStart model

## Error in model.frame.default(formula = ~B_plt_t2_MgHa + MEASTIME_t2 +  : 
##   variable lengths differ (found for '(sstart)')
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   1735     600.64                            
## 2   1734     598.66  1 1.9884  5.7594 0.01651 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 17999.63
## 2    2a 17995.87
## 3    2b 18000.53
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## tau    -0.851806   0.350036  -2.433  0.01505 *  
## alpha   0.596415   0.042420  14.060  < 2e-16 ***
## A     313.504594  50.186713   6.247 5.26e-10 ***
## k     179.346930  35.549874   5.045 5.01e-07 ***
## p       0.024058   0.008757   2.747  0.00607 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5876 on 1734 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.467e-06
##   (18 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1734     645.18                                
## 2   1733     592.96  1 52.222  152.63 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2a 17995.87
## 2     3 18126.02
## 3     4 17981.24

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau    -0.87412    0.34288  -2.549   0.0109 *  
## alpha   0.59872    0.04208  14.227  < 2e-16 ***
## a      27.03865    4.19436   6.446 1.48e-10 ***
## b     136.75568   18.11257   7.550 6.98e-14 ***
## c     241.17341   35.91839   6.714 2.55e-11 ***
## d       1.48402    0.13904  10.673  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5849 on 1733 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (18 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2617     1396.7                                
## 2   2616     1367.2  1 29.553  56.548 7.493e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 28732.83
## 2     2 28678.80

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.7345     0.8110   0.906    0.365    
## alpha   0.4532     0.0565   8.021 1.56e-15 ***
## A     213.4846    40.2569   5.303 1.23e-07 ***
## k     149.0161    14.4932  10.282  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7229 on 2616 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.067e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   2616     1367.2                                 
## 2   2615     1366.1  1  1.0599  2.0289    0.1545    
## 3   2615     1366.8  0  0.0000                      
## 4   2614     1351.0  1 15.7949 30.5617 3.554e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 28678.80
## 2    2a 28678.77
## 3    2b 28680.04
## 4    2c 28651.58

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.83577    0.84704   0.987    0.324    
## alpha   0.45196    0.05499   8.218 3.21e-16 ***
## A     133.15226   26.79988   4.968 7.19e-07 ***
## k      75.15432    7.52220   9.991  < 2e-16 ***
## p       0.07982    0.01467   5.442 5.75e-08 ***
## s       1.75902    0.17763   9.903  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7189 on 2614 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.142e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2615     1381.0                                
## 2   2614     1348.8  1 32.212   62.43 4.031e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    2c 28651.58
## 2     3 28707.13
## 3     4 28647.29

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     0.84900    0.84964   0.999    0.318    
## alpha   0.45685    0.05461   8.365  < 2e-16 ***
## a      11.69323    2.46329   4.747 2.18e-06 ***
## b     104.61495   20.34549   5.142 2.92e-07 ***
## c     258.30931   37.51848   6.885 7.22e-12 ***
## d       1.65652    0.12460  13.294  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7183 on 2614 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1753     893.12                                
## 2   1752     852.89  1 40.224  82.628 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19820.05
## 2     2 19741.13

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.49123    1.46753   1.016 0.309701    
## alpha   0.60068    0.06033   9.957  < 2e-16 ***
## A     312.74968   91.61362   3.414 0.000655 ***
## k     219.15324   28.08087   7.804 1.02e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6977 on 1752 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.964e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1   1752     852.89                         
## 2   1751     852.69  1  0.204  0.4189 0.5176
##   model      AIC
## 1     2 19741.13
## 2    2a 19742.70
## 3    2b       NA
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     1.49123    1.46753   1.016 0.309701    
## alpha   0.60068    0.06033   9.957  < 2e-16 ***
## A     312.74968   91.61362   3.414 0.000655 ***
## k     219.15324   28.08087   7.804 1.02e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6977 on 1752 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.964e-06
##   (2 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1751     828.43                                
## 2   1750     790.40  1 38.027  84.194 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 19741.13
## 2     3 19692.03
## 3     4 19611.51

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## tau     2.33449    1.85609   1.258  0.20865    
## alpha   0.57698    0.05622  10.263  < 2e-16 ***
## a      12.02383    3.70753   3.243  0.00120 ** 
## b      93.63274   28.58260   3.276  0.00107 ** 
## c     137.55008    7.17906  19.160  < 2e-16 ***
## d       1.09309    0.05382  20.312  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6721 on 1750 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1    424     163.07                               
## 2    423     146.44  1  16.63  48.035 1.57e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4280.845
## 2     2 4236.917

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.2772     0.6406   0.433  0.66539    
## alpha   0.8452     0.1103   7.661 1.27e-13 ***
## A      97.9714    18.4871   5.299 1.87e-07 ***
## k      53.0581    19.0692   2.782  0.00564 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5884 on 423 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 1.825e-06
##   (24 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_M334,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_M334,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     2 4236.917
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.2772     0.6406   0.433  0.66539    
## alpha   0.8452     0.1103   7.661 1.27e-13 ***
## A      97.9714    18.4871   5.299 1.87e-07 ***
## k      53.0581    19.0692   2.782  0.00564 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5884 on 423 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 1.825e-06
##   (24 observations deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

model selection 3

## Error in nls(f_3, data = G_M334, start = c(tau = tau.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_4, data = G_M334, start = c(tau = tau.start, alpha = alpha.start,  : 
##   Convergence failure: singular convergence (7)
##   model      AIC
## 1     2 4236.917
## 2     3       NA
## 3     4       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau     0.2772     0.6406   0.433  0.66539    
## alpha   0.8452     0.1103   7.661 1.27e-13 ***
## A      97.9714    18.4871   5.299 1.87e-07 ***
## k      53.0581    19.0692   2.782  0.00564 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5884 on 423 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 1.825e-06
##   (24 observations deleted due to missingness)

summary

simple log-normal model: does not fit
log-normal alpha model: does not fit

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    214     80.493                              
## 2    213     77.386  1 3.1072  8.5523 0.003824 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2156.928
## 2     2 2150.386

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.5816     0.5385  -2.937 0.003677 ** 
## alpha   0.4666     0.1455   3.207 0.001550 ** 
## A     235.0957    65.5828   3.585 0.000418 ***
## k     112.0187    30.9615   3.618 0.000371 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6028 on 213 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.283e-06
##   (3 observations deleted due to missingness)

summary

simple model: fits
alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    213     77.386                          
## 2    212     77.224  1 0.16244  0.4459  0.505
##   model      AIC
## 1     2 2150.386
## 2    2a 2151.930
## 3    2b 2152.190
## 4    2c       NA

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.5816     0.5385  -2.937 0.003677 ** 
## alpha   0.4666     0.1455   3.207 0.001550 ** 
## A     235.0957    65.5828   3.585 0.000418 ***
## k     112.0187    30.9615   3.618 0.000371 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6028 on 213 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.283e-06
##   (3 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)   
## 1    212     76.519                             
## 2    211     72.714  1  3.805  11.041 0.00105 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 2150.386
## 2     3 2149.940
## 3     4 2140.872

## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * tau/100) * (1 - alpha * 
##     B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## tau    -1.5408     0.5351  -2.880 0.004391 ** 
## alpha   0.5053     0.1373   3.681 0.000295 ***
## a      22.4320     6.3018   3.560 0.000459 ***
## b     115.3948    27.5776   4.184 4.20e-05 ***
## c     156.2468    22.9600   6.805 1.03e-10 ***
## d       1.0795     0.2035   5.305 2.84e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.587 on 211 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

simple log-normal model: fits
log-normal alpha model: fits

predict and plot

plotting 2

Fitted parameters

Best / selected models by ecoprovince

Ecoprovince	Ecoregion	Sel.Mod.2	Sel.Mod.3	Best.Mod
211	Northeastern Mixed Forest	2b	4	4
212	Laurentian Mixed Forest	2b	4	4
221	Eastern Broadleaf Forest	2a	4	4
222	Midwest Broadleaf Forest	2a	4	4
223	Central Interior Broadleaf Forest	2b	4	4
231	Southeastern Mixed Forest	2a	2a	2a
232	Outer Coastal Plain Mixed Forest	2b	2b	2b
234	Lower Mississippi Riverine Forest	2	2	2
242	Pacific Lowland Mixed Forest	NA	NA	NA
251	Prairie Parkland (Temperate)	2a	2a	2a
255	Prairie Parkland (Subtropical)	2	4	4
261	California Coastal Chaparral Forest and Shrub	NA	NA	NA
262	California Dry Steppe	NA	NA	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	2a	2a	2a
313	Colorado Plateau Semi-Desert	1	3	3
315	Southwest Plateau and Plains Dry Steppe and Shrub	NA	NA	NA
321	Chihuahuan Semi-Desert	NA	NA	NA
322	American Semidesert and Desert	NA	NA	NA
331	Great Plains/Palouse Dry Steppe	NA	NA	NA
332	Great Plains Steppe	2	2	2
341	Intermountain Semi-Desert and Desert	NA	NA	NA
342	Intermountain Semi-Desert	NA	NA	NA
411	Everglades	NA	NA	NA
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	2a	4	4
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	2c	4	4
M223	Ozark Broadleaf Forest Meadow	2a	2a	2a
M231	Ouachita Mixed Forest	2	2	2
M242	Cascade Mixed Forest	2b	4	4
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	2a	2a	2a
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	NA	NA	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	2a	4	4
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	2a	4	4
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	2c	4	4
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	2	4	4
M334	Black Hills Coniferous Forest	2	2	2
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	2	4	4

table by ecoprovince

Ecoprovince	Ecoregion	region	n.obs	n.plots	tau	tau.variance	tau.2.5	tau.97.5	alpha	alpha.variance	alpha.2.5	alpha.97.5	A	A.2.5	A.97.5	k	k.2.5	k.97.5	a	a.2.5	a.97.5	b	b.2.5	b.97.5	c	c.2.5	c.97.5	d	d.2.5	d.97.5
211	Northeastern Mixed Forest	east	6884	2879	0.8128805	0.0341550	0.4505946	1.1751665	0.8315403	0.0007698	0.7771511	0.8859295	267.35244	219.35952	315.3454	87.16041	63.848690	110.47212	31.22968	27.877587	34.58178	112.93234	102.35431	123.51038	123.6601	112.13157	135.18857	1.0673927	0.9722764	1.1625091
212	Laurentian Mixed Forest	east	22685	9493	1.0710340	0.0114002	0.8617530	1.2803150	0.7732144	0.0006389	0.7236709	0.8227579	115.78050	108.52419	123.0368	40.57330	37.341870	43.80472	22.95843	21.324590	24.59227	67.52314	64.47797	70.56831	103.1003	98.85456	107.34606	1.0873191	1.0294815	1.1451566
221	Eastern Broadleaf Forest	east	7307	3560	0.1986788	0.0127951	-0.0230617	0.4204193	0.8862948	0.0007294	0.8333532	0.9392364	297.82149	264.84583	330.7972	36.53118	21.221548	51.84081	46.50096	25.983421	67.01851	143.42164	118.24029	168.60298	119.2359	103.41338	135.05839	1.1069755	0.8700791	1.3438719
222	Midwest Broadleaf Forest	east	5846	2589	1.0625381	0.0439447	0.6515814	1.4734947	0.8721285	0.0018779	0.7871746	0.9570824	194.67994	169.43512	219.9248	40.40127	26.686540	54.11599	19.41594	12.154770	26.67712	96.66094	86.10982	107.21207	101.2566	92.41588	110.09733	1.0247052	0.8850278	1.1643826
223	Central Interior Broadleaf Forest	east	10006	3860	0.9546737	0.0122188	0.7379941	1.1713534	0.7913140	0.0007280	0.7384252	0.8442028	128.12523	118.95212	137.2983	32.43433	30.544669	34.32400	14.36005	-34.143582	62.86369	100.63809	50.20456	151.07162	118.7396	95.12609	142.35311	1.5526382	0.8475389	2.2577374
231	Southeastern Mixed Forest	east	12844	5935	1.2963478	0.0145029	1.0602901	1.5324056	0.7183089	0.0004146	0.6783943	0.7582235	220.17657	207.14256	233.2106	42.72274	38.206364	47.23911	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
232	Outer Coastal Plain Mixed Forest	east	13167	6463	0.7915440	0.0179347	0.5290391	1.0540489	0.6700200	0.0005556	0.6238177	0.7162223	206.16286	187.32559	225.0001	41.26733	35.663943	46.87072	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
234	Lower Mississippi Riverine Forest	east	1344	759	0.5256142	0.1674543	-0.2771902	1.3284185	0.7999862	0.0033505	0.6864285	0.9135439	478.26877	317.43343	639.1041	153.20836	92.986251	213.43046	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
242	Pacific Lowland Mixed Forest	west	85	85	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
251	Prairie Parkland (Temperate)	east	2290	903	0.4025611	0.0477957	-0.0261705	0.8312927	0.7155331	0.0048541	0.5789034	0.8521628	148.57344	128.51110	168.6358	5.24468	-5.375071	15.86443	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
255	Prairie Parkland (Subtropical)	east	714	318	-0.3313144	0.1933208	-1.1945585	0.5319296	0.5607660	0.0110571	0.3543162	0.7672159	317.92075	170.63777	465.2037	133.30362	65.298767	201.30848	11.80379	8.071868	15.53571	88.95895	68.86844	109.04946	58.2985	48.40726	68.18973	1.0552552	0.8693319	1.2411786
261	California Coastal Chaparral Forest and Shrub	west	26	26	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
262	California Dry Steppe	west	0	0	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	west	159	157	1.7516497	6.5664031	-3.3107992	6.8140987	0.8326216	0.0596171	0.3502495	1.3149937	15896.57299	-23729.49974	55522.6457	5997.12443	-9642.323051	21636.57192	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
313	Colorado Plateau Semi-Desert	west	218	218	-1.4503531	0.3524055	-2.6205414	-0.2801648	NA	NA	NA	NA	277.89641	59.74344	496.0494	159.09011	32.903856	285.27637	40.15842	16.002996	64.31384	148.91133	71.48995	226.33270	142.7671	125.62629	159.90790	0.6409271	0.4552203	0.8266338
315	Southwest Plateau and Plains Dry Steppe and Shrub	west	4	4	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
321	Chihuahuan Semi-Desert	west	9	9	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
322	American Semidesert and Desert	west	3	3	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
331	Great Plains/Palouse Dry Steppe	west	331	255	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
332	Great Plains Steppe	west	232	128	0.4762293	2.5216695	-2.6547219	3.6071806	0.6443436	0.0858053	0.0667941	1.2218931	502.59644	-693.17910	1698.3720	360.75928	-562.768438	1284.28699	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
341	Intermountain Semi-Desert and Desert	west	66	64	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
342	Intermountain Semi-Desert	west	124	123	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
411	Everglades	east	96	63	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	east	6778	3008	0.7210269	0.0260032	0.4049164	1.0371373	0.8165966	0.0005035	0.7726088	0.8605844	311.62395	275.78961	347.4583	106.27770	86.667211	125.88819	11.86910	6.238289	17.49991	156.98730	135.68083	178.29377	207.6905	155.55597	259.82507	1.7226645	1.5001895	1.9451395
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	east	8186	3765	0.9934830	0.0154443	0.7498705	1.2370956	0.8984551	0.0011323	0.8324930	0.9644173	154.79938	145.99431	163.6045	44.43699	39.737017	49.13696	49.42999	24.556832	74.30314	102.10729	77.35940	126.85518	100.6116	94.35973	106.86354	1.1053708	0.8527202	1.3580215
M223	Ozark Broadleaf Forest Meadow	east	893	348	0.0477424	0.0685395	-0.4660799	0.5615648	0.9033564	0.0052962	0.7605248	1.0461880	225.89814	176.32294	275.4733	51.43265	27.365362	75.49995	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M231	Ouachita Mixed Forest	east	1009	496	0.4620608	0.1889160	-0.3909092	1.3150308	0.7762262	0.0070908	0.6109745	0.9414779	306.46634	204.28218	408.6505	133.47106	82.495978	184.44613	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M242	Cascade Mixed Forest	west	3303	3286	0.5900829	0.4555005	-0.7331980	1.9133639	1.0753087	0.0048303	0.9390411	1.2115764	536.31143	366.60451	706.0184	119.02407	98.879928	139.16821	0.00000	-10.616952	10.61695	467.63578	316.19522	619.07633	581.4147	381.08599	781.74336	2.0957100	1.8323621	2.3590578
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	west	1993	1828	7.8784574	19.1671377	-0.7075676	16.4644824	0.6235532	0.0122832	0.4061984	0.8409080	130.60786	34.85927	226.3564	90.96584	55.156230	126.77545	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	west	30	26	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	west	367	367	-1.8270607	0.1225249	-2.4835133	-1.1706081	0.5964045	0.0165444	0.3341790	0.8586300	1027.37948	-762.41454	2817.1735	568.28926	-653.279611	1789.85813	42.68917	20.960445	64.41789	180.73752	99.98778	261.48725	177.7659	97.36014	258.17169	0.9807269	0.5729790	1.3884749
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	west	1757	1757	-0.8741218	0.1175653	-1.5466199	-0.2016237	0.5987195	0.0017710	0.5161802	0.6812588	313.50459	215.07174	411.9375	179.34693	109.621788	249.07207	27.03865	18.812107	35.26519	136.75568	101.23088	172.28048	241.1734	170.72545	311.62137	1.4840181	1.2113066	1.7567296
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	west	2621	2611	0.8489972	0.7218949	-0.8170458	2.5150402	0.4568543	0.0029828	0.3497617	0.5639469	133.15226	80.60113	185.7034	75.15432	60.404252	89.90438	11.69323	6.863029	16.52342	104.61495	64.72005	144.50985	258.3093	184.74038	331.87824	1.6565189	1.4121862	1.9008515
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	west	1758	1747	2.3344926	3.4450582	-1.3058885	5.9748736	0.5769754	0.0031608	0.4667081	0.6872428	312.74968	133.06615	492.4332	219.15324	164.077704	274.22878	12.02383	4.752172	19.29549	93.63274	37.57311	149.69237	137.5501	123.46966	151.63051	1.0930900	0.9875411	1.1986390
M334	Black Hills Coniferous Forest	west	451	179	0.2772480	0.4103689	-0.9819086	1.5364046	0.8451811	0.0121699	0.6283424	1.0620199	97.97135	61.63333	134.3094	53.05812	15.576023	90.54022	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	west	220	220	-1.5407977	0.2862822	-2.5955330	-0.4860625	0.5053432	0.0211720	0.2347287	0.7759577	235.09566	105.82124	364.3701	112.01875	50.988548	173.04894	22.43196	10.009441	34.85447	115.39477	61.03188	169.75766	156.2468	110.98635	201.50728	1.0795052	0.6783650	1.4806453

parameter variance co-variance

##                tau         alpha           a            b            c
## tau    0.034154968 -3.293976e-05 -0.17390829 -0.793823844 -0.079889622
## alpha -0.006423996  7.697974e-04  0.00263179  0.005057415 -0.002472449
## a     -0.550302776  5.547168e-02  2.92403993  1.052106639 -3.656498436
## b     -0.796006558  3.378001e-02  0.11402171 29.117970738 18.900890109
## c     -0.073504706 -1.515273e-02 -0.36360133  0.595598266 34.585699132
## d     -0.085697703  3.471544e-03 -0.56240022  0.570005584  0.910961614
##                   d
## tau   -7.684697e-04
## alpha  4.673493e-06
## a     -4.666248e-02
## b      1.492417e-01
## c      2.599435e-01
## d      2.354297e-03

##               tau         alpha             a            b            c
## tau    0.01140025  0.0004251389 -0.0437925935 -0.131046828 -0.025538513
## alpha  0.15752878  0.0006388922 -0.0002584548 -0.002546829 -0.001535693
## a     -0.49204748 -0.0122668871  0.6948210451 -0.011936079 -0.551432166
## b     -0.79000659 -0.0648555853 -0.0092169364  2.413666428  1.726771735
## c     -0.11042226 -0.0280484538 -0.3054033536  0.513114744  4.692060723
## d     -0.02407672 -0.0069386385 -0.6657573057  0.464024636  0.811153380
##                   d
## tau   -7.585637e-05
## alpha -5.175181e-06
## a     -1.637533e-02
## b      2.127243e-02
## c      5.184684e-02
## d      8.707130e-04

##               tau         alpha             a             b             c
## tau    0.01279505  0.0001236697 -1.710918e-01 -3.834621e-01  -0.027801875
## alpha  0.04048267  0.0007293676  7.656677e-04  5.272259e-04  -0.001632104
## a     -0.14451297  0.0027087298  1.095476e+02 -1.189418e+02 -59.265887462
## b     -0.26390421  0.0015197371 -8.846638e-01  1.650099e+02  85.926507053
## c     -0.03045101 -0.0074872641 -7.015394e-01  8.287447e-01  65.148239726
## d      0.02789528  0.0075874415 -9.289982e-01  9.309494e-01   0.901522674
##                   d
## tau    3.813172e-04
## alpha  2.476299e-05
## a     -1.175035e+00
## b      1.445159e+00
## c      8.793516e-01
## d      1.460391e-02

##               tau         alpha            a             b            c
## tau    0.04394466  0.0015084853 -0.179346620  -0.694574424 -0.027812045
## alpha  0.16605333  0.0018779363 -0.004808419  -0.009751327 -0.006264714
## a     -0.23098100 -0.0299569781 13.719166707 -10.991568329 -9.067076591
## b     -0.61561600 -0.0418087783 -0.551365984  28.967542723 15.126501182
## c     -0.02941947 -0.0320564803 -0.542823246   0.623214684 20.337143839
## d      0.04421864 -0.0008452601 -0.865739099   0.679738516  0.852702873
##                   d
## tau    6.604526e-04
## alpha -2.609841e-06
## a     -2.284726e-01
## b      2.606639e-01
## c      2.739844e-01
## d      5.076523e-03

##               tau         alpha            a             b             c
## tau    0.01221880  0.0005246004  -0.17767176 -6.604723e-02  2.095623e-02
## alpha  0.17589552  0.0007279794  -0.01386273  9.500917e-03  2.994822e-03
## a     -0.06495815 -0.0207643759 612.26706998 -6.327252e+02 -2.304800e+02
## b     -0.02322334  0.0136864379  -0.99386905  6.619590e+02  2.509666e+02
## c      0.01573773  0.0092141415  -0.77322540  8.097366e-01  1.451153e+02
## d      0.05479186  0.0187823639  -0.97922104  9.843806e-01  8.797111e-01
##                   d
## tau    0.0021785960
## alpha  0.0001822872
## a     -8.7156057856
## b      9.1101387099
## c      3.8119141288
## d      0.1293876360

##               tau         alpha            A            k             p
## tau    0.01450285  0.0001949633 -0.556054599 -0.003391909  1.483923e-05
## alpha  0.07950344  0.0004146487 -0.002302665 -0.001079011 -1.496585e-06
## A     -0.69439093 -0.0170060718 44.215374190 10.766491368  3.104088e-02
## k     -0.01222416 -0.0229978476  0.702731089  5.308804758  1.667267e-02
## p      0.01623981 -0.0096862943  0.615239101  0.953681138  5.757142e-05

##               tau         alpha            A            k             s
## tau    0.01793470  0.0001487194 -0.714972319 -0.006000287 -1.252955e-04
## alpha  0.04711369  0.0005555804  0.001985514 -0.001042707 -6.050837e-06
## A     -0.55553898  0.0087654029 92.353919166 22.803429480 -2.345681e-01
## k     -0.01567346 -0.0154749304  0.830065323  8.171851420 -8.801539e-02
## s     -0.02849401 -0.0078182057 -0.743372435 -0.937699133  1.078127e-03

##                tau        alpha            A             k
## tau    0.167454328  0.001355136  -17.1873405   -0.07518848
## alpha  0.057211002  0.003350503   -0.1997146   -0.10347624
## A     -0.512319070 -0.042085718 6721.0935598 2157.77792059
## k     -0.005985614 -0.058235955    0.8574175  942.29920519

##               tau        alpha           A           k            p
## tau    0.04779568  0.003696598  -1.5199537 -0.16251893 -0.106163461
## alpha  0.24269117  0.004854091  -0.0675872 -0.01053084 -0.006856526
## A     -0.67958786 -0.094824393 104.6600399 42.91056877 28.320759668
## k     -0.13727343 -0.027911676   0.7745522 29.32555886 19.521808318
## p     -0.13466118 -0.027290521   0.7676727  0.99967431 13.003993123

##               tau        alpha            a            b           c
## tau    0.19332077  0.007344857 -0.498615073  -4.19255053 -0.06671220
## alpha  0.15886342  0.011057077  0.000975675  -0.03706817 -0.02010617
## a     -0.59660668  0.004881429  3.613067354   9.03537112 -1.87751391
## b     -0.93184237 -0.034449620  0.464527443 104.71121089  8.74377683
## c     -0.03011686 -0.037953596 -0.196059915   0.16960793 25.38122913
## d     -0.03198883 -0.064081241 -0.427313399   0.11886019  0.83381407
##                   d
## tau   -0.0013319170
## alpha -0.0006381029
## a     -0.0769173197
## b      0.1151788166
## c      0.3978003365
## d      0.0089676615

##              tau       alpha             A             k             p
## tau    6.5664031  0.07181837 -1.285430e+04  2.219144e+03 -6.258973e-04
## alpha  0.1147854  0.05961707  3.499880e+02  2.097498e+02 -3.616051e-05
## A     -0.2500923  0.07146340  4.023169e+08  1.482250e+08 -4.322236e+01
## k      0.1093949  0.10851548  9.334968e-01  6.266846e+07 -1.793040e+01
## p     -0.1011995 -0.06136043 -8.928191e-01 -9.384361e-01  5.825345e-06

##            tau           a             b           c            d
## tau  0.3524055  -5.7246279  -22.06300480   0.5913954  0.001058122
## a   -0.7869475 150.1621212  309.82373329 -14.2180384 -0.299473936
## b   -0.9462740   0.6437364 1542.59841013 -15.3030414 -0.164524650
## c    0.1145671  -0.1334329   -0.04480790  75.6124585  0.544092506
## d    0.0189200  -0.2594093   -0.04446428   0.6641754  0.008875373

##              tau       alpha             A             k
## tau    2.5216695 0.069998493 -3.814150e+02   -109.227617
## alpha  0.1504831 0.085805282  4.572344e-01      3.437316
## A     -0.3960375 0.002573738  3.678196e+05 274225.961775
## k     -0.1468489 0.025052135  9.653247e-01 219399.393626

##               tau         alpha            a             b            c
## tau    0.02600316 -2.761285e-05 -0.034764631  -0.873034738  -0.07981265
## alpha -0.00763118  5.035155e-04  0.002764817  -0.003385973  -0.03071582
## a     -0.07505497  4.289581e-02  8.250688464 -19.708703824 -54.50843225
## b     -0.49811855 -1.388326e-02 -0.631287579 118.133058667 249.18479349
## c     -0.01861053 -5.147020e-02 -0.713540632   0.862056883 707.29367745
## d     -0.01897962 -4.291364e-02 -0.868218914   0.838638992   0.95816406
##                   d
## tau   -0.0003473411
## alpha -0.0001092842
## a     -0.2830283113
## b      1.0344662314
## c      2.8919801589
## d      0.0128798583

##               tau         alpha             a             b             c
## tau    0.01544427  0.0002536698  -0.196584244 -2.457777e-01  -0.033877302
## alpha  0.06066054  0.0011322901   0.000362471  1.665029e-03  -0.001163569
## a     -0.12466659  0.0008489447 161.001490491 -1.533477e+02 -18.532972265
## b     -0.15665222  0.0039194092  -0.957282318  1.593839e+02  20.752286053
## c     -0.08547293 -0.0108421847  -0.457966364  5.154032e-01  10.171689408
## d      0.02572335  0.0068963954  -0.951579959  9.424641e-01   0.667187808
##                   d
## tau    4.120174e-04
## alpha  2.990925e-05
## a     -1.556198e+00
## b      1.533528e+00
## c      2.742516e-01
## d      1.661150e-02

##               tau        alpha            A            k             p
## tau    0.06853953  0.000325955  -4.03057365  -0.27242629 -8.957156e-04
## alpha  0.01710824  0.005296189   0.05919583  -0.01203524 -4.468643e-05
## A     -0.60950072  0.032202330 638.03446216 254.39202464  8.047295e-01
## k     -0.08485817 -0.013486158   0.82129016 150.37291073  5.087456e-01
## p     -0.07711058 -0.013839115   0.71802949   0.93504024  1.968662e-03

##                tau         alpha            A            k
## tau    0.188915964  0.0001524564  -13.7273187   -0.7699364
## alpha  0.004165477  0.0070907629   -0.2150236   -0.2291201
## A     -0.606550870 -0.0490405568 2711.2422008 1121.5829707
## k     -0.068196498 -0.1047510125    0.8292563  674.7096641

##                tau         alpha            a             b             c
## tau    0.455500485  0.0003265189 -0.069700462  -47.94614555     0.1435947
## alpha  0.006961115  0.0048302571 -0.001789894    0.09259516    -0.1525302
## a     -0.019072122 -0.0047560897 29.321381165  -77.65294702  -327.1580595
## b     -0.919760452  0.0172491868 -0.185665489 5965.80551129  2889.1880122
## c      0.002082373 -0.0214800434 -0.591330013    0.36610509 10439.2904028
## d      0.020769211 -0.0133973082 -0.787866075    0.30434551     0.9421937
##                   d
## tau    0.0018827235
## alpha -0.0001250618
## a     -0.5730159677
## b      3.1573560191
## c     12.9299789035
## d      0.0180403195

##                 tau       alpha            A            k             p
## tau   19.1671377313  0.07485946 -209.0074296  -0.74797970 -8.433607e-05
## alpha  0.1542809916  0.01228319   -0.7054270  -0.04442519 -9.261757e-05
## A     -0.9778319433 -0.13036996 2383.6239698 181.85591933  2.626134e-01
## k     -0.0093567522 -0.02195268    0.2039964 333.40499318  6.009473e-01
## p     -0.0005107549 -0.02215724    0.1426185   0.87262612  1.422474e-03

##                tau        alpha             a            b            c
## tau    0.111425743 0.0002768889 -2.529440e+00  -10.4807058   -1.5065987
## alpha  0.006448933 0.0165443521  1.988780e-01    0.3286231    0.3070966
## a     -0.685816618 0.1399388646  1.220807e+02  172.2963033   -0.3624131
## b     -0.764658023 0.0622218146  3.797711e-01 1686.0134031 1062.0122181
## c     -0.110389609 0.0583947139 -8.022387e-04    0.6325901 1671.6804443
## d     -0.096351180 0.0339530989 -1.484090e-01    0.5268294    0.9183837
##                   d
## tau   -0.0066685434
## alpha  0.0009054938
## a     -0.3399891459
## b      4.4851989129
## c      7.7854190641
## d      0.0429894959

##                tau        alpha           a            b             c
## tau    0.117565294 -0.000447291 -1.08948293  -5.45404960    0.02726223
## alpha -0.030998552  0.001770999  0.02985268   0.03820798   -0.02760001
## a     -0.757556422  0.169125171 17.59267006  38.15338208  -45.61992825
## b     -0.878212045  0.050126191  0.50221194 328.06526847  280.79535627
## c      0.002213630 -0.018259256 -0.30281113   0.43161140 1290.13088760
## d      0.009871542 -0.034677596 -0.44745292   0.37590998    0.92231721
##                   d
## tau    0.0004706267
## alpha -0.0002029131
## a     -0.2609547462
## b      0.9467078193
## c      4.6062677563
## d      0.0193332096

##               tau        alpha           a            b            c
## tau    0.72189485  0.001706874 -1.81860986 -16.50260979   -2.5940486
## alpha  0.03678362  0.002982773  0.01413437  -0.01779304   -0.1041115
## a     -0.86893434  0.105063237  6.06779937  38.53960620  -15.6004142
## b     -0.95465737 -0.016012970  0.76899504 413.93891216  265.7892705
## c     -0.08137592 -0.050809308 -0.16880111   0.34819626 1407.6361975
## d     -0.05324810 -0.094018080 -0.30457223   0.27345268    0.9094210
##                   d
## tau   -0.0056373301
## alpha -0.0006398141
## a     -0.0934842063
## b      0.6932384732
## c      4.2515034037
## d      0.0155261823

##               tau        alpha            a            b           c
## tau    3.44505817  0.003520774 -6.729276173 -52.81352651 -0.15008650
## alpha  0.03373972  0.003160798  0.008731308  -0.02811251 -0.01063845
## a     -0.97787912  0.041888617 13.745792939 102.87060477 -0.82618681
## b     -0.99550903 -0.017494420  0.970743994 816.96483683 12.38096064
## c     -0.01126357 -0.026358017 -0.031040308   0.06033722 51.53884559
## d     -0.02568570 -0.098885667 -0.076109778   0.04570799  0.80089205
##                   d
## tau   -0.0025656358
## alpha -0.0002991831
## a     -0.0151855555
## b      0.0703070926
## c      0.3094187709
## d      0.0028960807

##               tau        alpha            A            k
## tau    0.41036895  0.008872732  -7.84008531  -0.31934954
## alpha  0.12555261  0.012169947  -0.03070134   0.07153567
## A     -0.66201025 -0.015053731 341.77292767 264.57032727
## k     -0.02614253  0.034005321   0.75048304 363.63262478

##               tau       alpha           a             b           c
## tau    0.28628223 -0.01338815 -2.83343963 -13.916816713  -0.8430314
## alpha -0.18227141  0.01884558  0.23803779   0.987256814   0.1778299
## a     -0.84033709  0.27515529 39.71243136 130.831786659  -5.8229042
## b     -0.94316230  0.26077686  0.75282452 760.523358217 139.7773938
## c     -0.06862364  0.05641925 -0.04024423   0.220753656 527.1637135
## d      0.04196025  0.06218896 -0.25485915   0.006191206   0.7517345
##                  d
## tau    0.004568621
## alpha  0.001737272
## a     -0.326823523
## b      0.034744122
## c      3.512263217
## d      0.041409469

plot tau

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

plot alpha (biomass compensation effect)

plot A (asymptote of B)

## Warning: Removed 12 rows containing missing values (`geom_point()`).

plot k (stand age at half biomass asymptote)

## Warning: Removed 12 rows containing missing values (`geom_point()`).

FIA NLS Models: Biomass vs. Stand Age

JAH

2023-07-12

Background

211 - Northeastern Mixed Forest

model selection 1

summary

model selection 2

summary

model selection 3

summary

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

summary

model selection 2

summary

model selection 3

summary

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

summary

model selection 2

summary

model selection 3

summary

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

summary

model selection 2

summary

model selection 3

summary

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

summary

model selection 2

summary

model selection 3

summary

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

summary

model selection 2

summary

model selection 3

summary

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

summary

model selection 2

summary

model selection 3

summary

predict and plot

plotting 2

234 - lower Mississippi Riverine Forest

model selection 1

summary

model selection 2

summary

model selection 3

summary

predict and plot

242 - Pacific Lowland Mixed Forest

model selection 1

summary

model selection 2

summary